How to copy files while not modifying the file creation times at all?

Robocopy preserves timestamps by default. You can get it for XP in the Windows Server 2003 Resource Kit.

example:

robocopy C:\ E:\ /E

If you aren't comfortable with the command line, Robocopy GUI makes it even easier.

Another copy utility which can preserve timestamps is XXCOPY:

Zip the files. Then extract the .zip to the destination. Seriously.

Windows Explorer doesn't offer any "Paste Special" menu option, so you only have the normal paste behavior.

I'd like to think there may be a shell extension written by someone somewhere, which could add a "Paste with creation times" menu option, but I've not found one.